1. Mining AltCoins? Isn't that illegal, like printing counterfeit money?
2. Bitcoin (and altcoins) are just code? What value do they have?
3. OMG! Your trying to counterfeit money!
1 & 3 are somewhat the same, and I have only one basic answer..
To counterfeit is to try and reproduce something already known.. If you get a printing press, and try running off a stack of USD and attempt to pass them as legit, that is counterfeiting.. Creating your own currency is not the same and is fairly regular practice.. For simplest comparison, say it's no different then a credit card company issuing air miles credits. They are a way of accounting someone's stake, and are accepted in return for goods or services just like cash and are perfectly legal. Crypto just takes it a step further, removing a centralized issuer and giving everyone the opportunity to participate in distribution and transaction clearing between parties.
2, yes just code.. but very powerful. Most people who do not understand crypto currencies have a reasonable grasp of what inflation in normal currencies means. Once you have explained point 1, and they are on board with the idea that it is a legal way to hold and transact value, you can then explain how by design BTC (alt's can be different in this way, so I'll stick to BTC) can be used as a hedge against fiat currency inflation. Which in many peoples minds is one thing that contributes to why this simple code carries significant value.
Kinda basic ideas, but hopefully that helps some..